Quick summation - Math question

[demon42]

inf.
------,
\ ' 9
/ , 10^i
------'
i = 1

Is this exactly equal to 1?

EDIT: i starts at 1, not 0

 

[dullard]

Originally posted by: demon42
inf.
------,
\ ' 9
/ , 10^i
------'
i = 0

Is this exactly equal to 1?

No. That won't be equal to 1.0. (You are off by a decimal point).

And why not just ask if 9.99999 = 10?

 

[blackdogdeek]

i think it equals lock

 

[So]

No, 10.

 

[jimbob200521]

No.

 

[jman19]

No.

 

[So]

if X is the sum:

i = 0; x = 9
i = 1; x = .9
i = 2; x = .09
i = 3; x = .009
and so on
9.999...

 

[demon42]

Originally posted by: dullard
No. That won't be equal to 1.0. (You are off by a decimal point).

And why not just ask if 9.99999 = 10?

sorry, i meant startig at i=1

i would have thought yes, given that the value is infinitely closer to 1... but that's just wrong?

 

[jman19]

Originally posted by: So
No, 10.

Nice edit I almost made the same mistake.

 

[dullard]

Originally posted by: demon42
sorry, i meant startig at i=1

Then yes, if you have an infinite number of terms, it is equal to 1. If you don't have an infinite number of terms, it is not equal to 1.

 

[So]

Originally posted by: jman19

Originally posted by: So
No, 10.

Nice edit I almost made the same mistake.

I am far from infallible.

But as soon as I looked at it for a moment, it was a "duh"

 

[demon42]

ah, cool, i thought maybe, but I wasn't sure

 

[Axoliien]

take the constant outside of your sum, and see what it resembles...

sum(i=0,2)
= 9/1 + 9/10 + 9/100
= 900/100 + 90/100 + 9/100
= 999/100
= 9(111/100)
= 9(100/100 + 10/100 + 1/100)
= 9(1/1 + 1/10 + 1/100)

Not too tough to figure out a series from there, I think...

Edit: Since it's from 1 to inf, just change your series calculation, I'm leaving the original cause I'm lazy.

 

[Aluvus]

Originally posted by: dullard
And why not just ask if 9.99999 = 10?

Or even sum(9/10^i) from i=1 to infinity.

Anyway, there are several proofs (and a good deal else) on Wikipedia. There was a thread in HT not too long ago, but damned if I can find it.

 

[DrPizza]

OMG! No idiots yet.
<pulls up lawnchair, starts the bbq and cracks open a beer>
<waits for idiots to swarm into this thread claiming that it's .000...001 less than 1>

Hmmm... on second thought, the title of the thread might just keep them away!